An extended Bayesian framework for atrial and ventricular activity separation in atrial fibrillation

An extended nonlinear Bayesian filtering framework is introduced for the analysis of atrial fibrillation (AF), in particular with single-channel electrocardiographical (ECG) recordings. It is suitable for simultaneously tracking the fundamental frequency of atrial fibrillatory waves (f-waves), and separating signals, linked to atrial and ventricular activity, during AF. In this framework, high-power ECG components, i.e., Q, R, S, and T waves, are modeled using sum of Gaussian functions. The atrial activity dynamical model is instead based on a trigonometrical function, with a fundamental frequency (the inverse of the dominant atrial cycle length), and its harmonics. The state variables of both dynamical models (QRS-T and f-waves) are hidden and, then estimated, sample by sample, using a Kalman smoother. Remarkably, the scheme is capable of separating ventricular and atrial activity signals, while contemporarily tracking the atrial fundamental frequency in time. The proposed method was evaluated using synthetic signals. In 290 ECGs in sinus rhythm from the PhysioNet PTB Diagnostic ECG Database, the P-waves were replaced with a synthetic f-wave. Broadband noise at different signal-to-noise ratio (SNR) (from 0 to 40 dB) was added to study the performance of the filter, under different SNR conditions. The results of the study demonstrated superior results in atrial and ventricular signal separation when compared with traditional average beat subtraction (ABS), one of the most widely used method for QRS-T cancellation (normalized mean square error = 0.045 for extended Kalman smoother (EKS) and 0.18 for ABS, SNR improvement was 21.1 dB for EKS and 12.2 dB for ABS in f-wave extraction). Various advantages of the proposed method have been addressed and demonstrated, including the problem of tracking the fundamental frequency of f-waves (root mean square error (RMSE) ≈ 0.03 ± 0.005 Hz for gradually changing frequency at SNR=15 dB) and of estimating robust QT/RR values during AF (RMSE ≈ 0.008 ± 0.001 at SNR = 10 dB, R 2 = 0.99).